PROJECT SUMMARY - TR&D3: INTRINSIC SURFACE MAPPING For brain imaging studies, surface mapping methods have played an important role in various scientific discoveries from tracking the maturation of adolescent brains to mapping gray matter atrophy patterns in Alzheimer's disease (AD). There are, however, two fundamental limitations in current surface mapping techniques. Firstly, current methods typically parameterize different brain surfaces with the unit sphere before their registration. The inevitable metric distortions during this parameterization step can lead to errors in the registration of brain anatomy and reduced power in the detection of disease induced changes. Secondly, current surface mapping tools such as FreeSurfer depend on geometric features that have limited accuracy in mapping high order brain regions and do not consider disease-related biological mechanisms. In this project, we will develop a novel computational framework to overcome these fundamental limitations. This novel approach builds upon our series of shape analysis work in the Laplace-Beltrami embedding space of anatomical surfaces. This embedding is isometric, so it eliminates the metric distortion due to spherical parameterization and resulting errors in the maps computed by spherical registration. This general framework also enables the incorporation of multimodal imaging features to compute diffeomorphic surface maps that improve the accuracy in aligning corresponding anatomy and functions of human brains. Overall there are three specific aims in this project. Aim 1. Development of the surface mapping software tools under the Riemannian metric optimization framework. In this aim, we will focus on developing a user friendly software toolset that implements the algorithms for Riemannian Metric Optimization on Surfaces (RMOS) in the LB embedding space. Aim 2. Development of novel RMOS surface mapping methods driven by rich contextual features. In this aim, we will develop a rich set of contextual features to drive the RMOS computational engine and provide more anatomically meaningful brain mapping results. Aim 3. Development of longitudinal surface mapping methods in the Laplace-Beltrami embedding space. In this aim, we will use the RMOS framework to develop novel methods for studying the longitudinal evolution of brain anatomy. All software tools developed in this project will be continuously distributed in our software called Metric Optimization for Computational Anatomy (MOCA) on LONIR website.